Acta Phys. -Chim. Sin. ›› 2018, Vol. 34 ›› Issue (6): 625-630.doi: 10.3866/PKU.WHXB201711071

Special Issue: 密度泛函理论中的化学概念特刊

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Levy Constrained Search in Fock Space: An Alternative Approach to Noninteger Electron Number

Paul W. AYERS1,*(),Mel LEVY2,3,4,*()   

  1. 1 Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
    2 Department of Physics, North Carolina A & T State University, Greensboro, NC 27411, USA
    3 Department of Chemistry, Duke University, Durham, NC 27708, USA
    4 Department of Chemistry, Tulane University, New Orleans, LA 70118, USA
  • Received:2017-09-25 Online:2018-06-15 Published:2018-03-20
  • Contact: Paul W. AYERS,Mel LEVY;


By extending the Levy wavefunction constrained search to Fock Space, one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons. For pure-state v-representable densities, the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble. In other cases, the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional. One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states (i.e., those that are not ground-state v-representable) are the stationary points of the Fock-space functional. However, a potential disadvantage of the Fock-space constrained search functional is that it is not convex.

Key words: Density functional theory, Levy constrained search functional, Fock space, Fractional electron number, Excited-state density functional theory, Universal density functional, Zero temperature grand canonical ensemble, Convexity